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  <title>第 6 章 光合气孔导度耦合模型 | 使用 R 语言分析 LI-6400 和 LI-6800 光合仪的数据</title>
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<ul class="summary">
<li><a href="./">R 软件与光合数据分析</a></li>

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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>欢迎</a></li>
<li class="chapter" data-level="" data-path="frontmatter.html"><a href="frontmatter.html"><i class="fa fa-check"></i>前言</a></li>
<li class="chapter" data-level="" data-path="copyright.html"><a href="copyright.html"><i class="fa fa-check"></i>版权</a></li>
<li class="chapter" data-level="1" data-path="intro.html"><a href="intro.html"><i class="fa fa-check"></i><b>1</b> R 软件与 Rstudio</a>
<ul>
<li class="chapter" data-level="1.1" data-path="intro.html"><a href="intro.html#rsoft"><i class="fa fa-check"></i><b>1.1</b> R 软件</a></li>
<li class="chapter" data-level="1.2" data-path="intro.html"><a href="intro.html#rstudiosoft"><i class="fa fa-check"></i><b>1.2</b> Rstudio</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="batch_question.html"><a href="batch_question.html"><i class="fa fa-check"></i><b>2</b> 批量处理光合测定数据</a>
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<li class="chapter" data-level="2.1" data-path="batch_question.html"><a href="batch_question.html#install_readphoto"><i class="fa fa-check"></i><b>2.1</b> 安装</a></li>
<li class="chapter" data-level="2.2" data-path="batch_question.html"><a href="batch_question.html#batch64"><i class="fa fa-check"></i><b>2.2</b> LI-6400 数据处理</a>
<ul>
<li class="chapter" data-level="2.2.1" data-path="batch_question.html"><a href="batch_question.html#li-6400-数据的整合6400combine"><i class="fa fa-check"></i><b>2.2.1</b> LI-6400 数据的整合{#6400combine}</a></li>
<li class="chapter" data-level="2.2.2" data-path="batch_question.html"><a href="batch_question.html#recompute6400"><i class="fa fa-check"></i><b>2.2.2</b> LI-6400 数据重计算</a></li>
</ul></li>
<li class="chapter" data-level="2.3" data-path="batch_question.html"><a href="batch_question.html#li-6800-数据的处理-6800data"><i class="fa fa-check"></i><b>2.3</b> LI-6800 数据的处理 {#6800data}</a>
<ul>
<li class="chapter" data-level="2.3.1" data-path="batch_question.html"><a href="batch_question.html#r-下-excel-格式读取的重计算-6800xlconnect"><i class="fa fa-check"></i><b>2.3.1</b> R 下 Excel 格式读取的重计算 {##6800xlconnect}</a></li>
<li class="chapter" data-level="2.3.2" data-path="batch_question.html"><a href="batch_question.html#python"><i class="fa fa-check"></i><b>2.3.2</b> 使用 Python 来处理</a></li>
<li class="chapter" data-level="2.3.3" data-path="batch_question.html"><a href="batch_question.html#python-r-batch"><i class="fa fa-check"></i><b>2.3.3</b> 批量处理 csv 文件</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="3" data-path="response_fit.html"><a href="response_fit.html"><i class="fa fa-check"></i><b>3</b> CO<sub>2</sub> 响应曲线的拟合</a>
<ul>
<li class="chapter" data-level="3.1" data-path="response_fit.html"><a href="response_fit.html#fvcb_mod"><i class="fa fa-check"></i><b>3.1</b> FvCB 模型</a></li>
<li class="chapter" data-level="3.2" data-path="response_fit.html"><a href="response_fit.html#co2_note"><i class="fa fa-check"></i><b>3.2</b> CO<sub>2</sub> 响应曲线测量的注意事项</a>
<ul>
<li class="chapter" data-level="3.2.1" data-path="response_fit.html"><a href="response_fit.html#model_3"><i class="fa fa-check"></i><b>3.2.1</b> 分段性</a></li>
<li class="chapter" data-level="3.2.2" data-path="response_fit.html"><a href="response_fit.html#note_detail"><i class="fa fa-check"></i><b>3.2.2</b> 测量注意事项</a></li>
</ul></li>
<li class="chapter" data-level="3.3" data-path="response_fit.html"><a href="response_fit.html#plantecophys"><i class="fa fa-check"></i><b>3.3</b> <code>plantecophys</code> 软件包</a></li>
<li class="chapter" data-level="3.4" data-path="response_fit.html"><a href="response_fit.html#fit6400"><i class="fa fa-check"></i><b>3.4</b> LI-6400XT CO<sub>2</sub> 响应曲线的拟合</a>
<ul>
<li class="chapter" data-level="3.4.1" data-path="response_fit.html"><a href="response_fit.html#fitaci_intro"><i class="fa fa-check"></i><b>3.4.1</b> fitaci 函数介绍</a></li>
</ul></li>
<li class="chapter" data-level="3.5" data-path="response_fit.html"><a href="response_fit.html#plantecophy_use"><i class="fa fa-check"></i><b>3.5</b> 使用 <code>plantecophys</code> 拟合 LI-6400XT CO<sub>2</sub> 响应曲线数据</a>
<ul>
<li class="chapter" data-level="3.5.1" data-path="response_fit.html"><a href="response_fit.html#data6400"><i class="fa fa-check"></i><b>3.5.1</b> 数据的前处理</a></li>
<li class="chapter" data-level="3.5.2" data-path="response_fit.html"><a href="response_fit.html#fitaci-p"><i class="fa fa-check"></i><b>3.5.2</b> 使用示例</a></li>
<li class="chapter" data-level="3.5.3" data-path="response_fit.html"><a href="response_fit.html#onpoint_fit"><i class="fa fa-check"></i><b>3.5.3</b> 使用 ‘onepoint’ 单独计算 V<sub>cmax</sub> 和 J<sub>max</sub></a></li>
<li class="chapter" data-level="3.5.4" data-path="response_fit.html"><a href="response_fit.html#multi_curve"><i class="fa fa-check"></i><b>3.5.4</b> 多条 CO<sub>2</sub> 响应曲线的拟合</a></li>
<li class="chapter" data-level="3.5.5" data-path="response_fit.html"><a href="response_fit.html#transition"><i class="fa fa-check"></i><b>3.5.5</b> <code>findCiTransition</code> 函数</a></li>
</ul></li>
<li class="chapter" data-level="3.6" data-path="response_fit.html"><a href="response_fit.html#c4"><i class="fa fa-check"></i><b>3.6</b> C4 植物光合</a>
<ul>
<li class="chapter" data-level="3.6.1" data-path="response_fit.html"><a href="response_fit.html#c4_sim"><i class="fa fa-check"></i><b>3.6.1</b> C4 植物光合速率的计算</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="4" data-path="stomotal_sim.html"><a href="stomotal_sim.html"><i class="fa fa-check"></i><b>4</b> 气孔导度模型的拟合</a>
<ul>
<li class="chapter" data-level="4.1" data-path="stomotal_sim.html"><a href="stomotal_sim.html#ballberry"><i class="fa fa-check"></i><b>4.1</b> BallBerry 模型</a></li>
<li class="chapter" data-level="4.2" data-path="stomotal_sim.html"><a href="stomotal_sim.html#bbleuning"><i class="fa fa-check"></i><b>4.2</b> BBLeuning 模型</a></li>
<li class="chapter" data-level="4.3" data-path="stomotal_sim.html"><a href="stomotal_sim.html#bboptifull"><i class="fa fa-check"></i><b>4.3</b> BBOptiFull 模型</a></li>
<li class="chapter" data-level="4.4" data-path="stomotal_sim.html"><a href="stomotal_sim.html#fitbb-p"><i class="fa fa-check"></i><b>4.4</b> <code>fitBB</code> 函数</a></li>
<li class="chapter" data-level="4.5" data-path="stomotal_sim.html"><a href="stomotal_sim.html#fitbbs"><i class="fa fa-check"></i><b>4.5</b> <code>fitBBs</code> 函数</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="stomotal_couple.html"><a href="stomotal_couple.html"><i class="fa fa-check"></i><b>5</b> 光合最优气孔导度耦合模型</a>
<ul>
<li class="chapter" data-level="5.1" data-path="stomotal_couple.html"><a href="stomotal_couple.html#farao"><i class="fa fa-check"></i><b>5.1</b> <code>FARAO</code> 函数</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="photo_stomo.html"><a href="photo_stomo.html"><i class="fa fa-check"></i><b>6</b> 光合气孔导度耦合模型</a>
<ul>
<li class="chapter" data-level="6.1" data-path="photo_stomo.html"><a href="photo_stomo.html#photosyn"><i class="fa fa-check"></i><b>6.1</b> <code>Photosyn</code> 函数</a>
<ul>
<li class="chapter" data-level="6.1.1" data-path="photo_stomo.html"><a href="photo_stomo.html#photo_exam"><i class="fa fa-check"></i><b>6.1.1</b> <code>Photosyn</code> 使用举例</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="photo_stomo.html"><a href="photo_stomo.html#photsyneb"><i class="fa fa-check"></i><b>6.2</b> <code>PhotosynEB</code> 函数</a></li>
<li class="chapter" data-level="6.3" data-path="photo_stomo.html"><a href="photo_stomo.html#photosyntuzet"><i class="fa fa-check"></i><b>6.3</b> <code>PhotosynTuzet</code> 函数</a>
<ul>
<li class="chapter" data-level="6.3.1" data-path="photo_stomo.html"><a href="photo_stomo.html#photosyntuzet_para"><i class="fa fa-check"></i><b>6.3.1</b> <code>PhotosynTuzet</code> 的参数</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="7" data-path="rhtovpd.html"><a href="rhtovpd.html"><i class="fa fa-check"></i><b>7</b> RHtoVPD 函数</a></li>
<li class="chapter" data-level="8" data-path="lrc_fit.html"><a href="lrc_fit.html"><i class="fa fa-check"></i><b>8</b> 光响应曲线的拟合</a>
<ul>
<li class="chapter" data-level="8.1" data-path="lrc_fit.html"><a href="lrc_fit.html#rec_mod"><i class="fa fa-check"></i><b>8.1</b> 直角双曲线模型</a>
<ul>
<li class="chapter" data-level="8.1.1" data-path="lrc_fit.html"><a href="lrc_fit.html#rec_fit"><i class="fa fa-check"></i><b>8.1.1</b> 直角双曲线模型的实现</a></li>
</ul></li>
<li class="chapter" data-level="8.2" data-path="lrc_fit.html"><a href="lrc_fit.html#nonrec-mod"><i class="fa fa-check"></i><b>8.2</b> 非直角双曲线模型</a>
<ul>
<li class="chapter" data-level="8.2.1" data-path="lrc_fit.html"><a href="lrc_fit.html#nonrec_mode_exam"><i class="fa fa-check"></i><b>8.2.1</b> 非直角双曲线模型的实现</a></li>
</ul></li>
<li class="chapter" data-level="8.3" data-path="lrc_fit.html"><a href="lrc_fit.html#lrc_exp"><i class="fa fa-check"></i><b>8.3</b> 指数模型</a>
<ul>
<li class="chapter" data-level="8.3.1" data-path="lrc_fit.html"><a href="lrc_fit.html#lrc_exp_exam"><i class="fa fa-check"></i><b>8.3.1</b> 指数模型的实现</a></li>
</ul></li>
<li class="chapter" data-level="8.4" data-path="lrc_fit.html"><a href="lrc_fit.html#rev_rec"><i class="fa fa-check"></i><b>8.4</b> 直角双曲线的修正模型</a>
<ul>
<li class="chapter" data-level="8.4.1" data-path="lrc_fit.html"><a href="lrc_fit.html#rev_rec_exam"><i class="fa fa-check"></i><b>8.4.1</b> 直角双曲线修正模型的实现</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="9" data-path="start_con.html"><a href="start_con.html"><i class="fa fa-check"></i><b>9</b> 关于非线性拟合的初始值</a>
<ul>
<li class="chapter" data-level="9.1" data-path="start_con.html"><a href="start_con.html#nlslm"><i class="fa fa-check"></i><b>9.1</b> nlsLM 解决方案</a></li>
<li class="chapter" data-level="9.2" data-path="start_con.html"><a href="start_con.html#plot_comp"><i class="fa fa-check"></i><b>9.2</b> 作图比对法</a>
<ul>
<li class="chapter" data-level="9.2.1" data-path="start_con.html"><a href="start_con.html#plot_exam"><i class="fa fa-check"></i><b>9.2.1</b> 实现过程</a></li>
<li class="chapter" data-level="9.2.2" data-path="start_con.html"><a href="start_con.html#show_demo"><i class="fa fa-check"></i><b>9.2.2</b> 直观展示</a></li>
</ul></li>
<li class="chapter" data-level="9.3" data-path="start_con.html"><a href="start_con.html#mult_try"><i class="fa fa-check"></i><b>9.3</b> 自动多次尝试法</a></li>
<li class="chapter" data-level="9.4" data-path="start_con.html"><a href="start_con.html#sum_start"><i class="fa fa-check"></i><b>9.4</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="anay_6800.html"><a href="anay_6800.html"><i class="fa fa-check"></i><b>10</b> LI-6800 的数据分析</a>
<ul>
<li class="chapter" data-level="10.1" data-path="anay_6800.html"><a href="anay_6800.html#data6800"><i class="fa fa-check"></i><b>10.1</b> 数据格式</a></li>
<li class="chapter" data-level="10.2" data-path="anay_6800.html"><a href="anay_6800.html#dif"><i class="fa fa-check"></i><b>10.2</b> LI-6800 与 LI-6400 使用时的差别</a></li>
<li class="chapter" data-level="10.3" data-path="anay_6800.html"><a href="anay_6800.html#notice"><i class="fa fa-check"></i><b>10.3</b> 光响应曲线注意事项</a></li>
<li class="chapter" data-level="10.4" data-path="anay_6800.html"><a href="anay_6800.html#other_light_response"><i class="fa fa-check"></i><b>10.4</b> 其他软件包的光响应曲线</a></li>
<li class="chapter" data-level="10.5" data-path="anay_6800.html"><a href="anay_6800.html#racir68"><i class="fa fa-check"></i><b>10.5</b> LI-6800 RACiR的测量与拟合</a></li>
<li class="chapter" data-level="10.6" data-path="anay_6800.html"><a href="anay_6800.html#racir-conifer"><i class="fa fa-check"></i><b>10.6</b> LI-6800 RACiR簇状叶的测量与拟合</a></li>
<li class="chapter" data-level="10.7" data-path="anay_6800.html"><a href="anay_6800.html#multi1"><i class="fa fa-check"></i><b>10.7</b> 多个速率的 RACiR 曲线研究</a>
<ul>
<li class="chapter" data-level="10.7.1" data-path="anay_6800.html"><a href="anay_6800.html#multi2"><i class="fa fa-check"></i><b>10.7.1</b> 光呼吸滞后模型</a></li>
<li class="chapter" data-level="10.7.2" data-path="anay_6800.html"><a href="anay_6800.html#code-photoresp"><i class="fa fa-check"></i><b>10.7.2</b> 光呼吸滞后性代码</a></li>
<li class="chapter" data-level="10.7.3" data-path="anay_6800.html"><a href="anay_6800.html#multi4"><i class="fa fa-check"></i><b>10.7.3</b> 数据的构造</a></li>
<li class="chapter" data-level="10.7.4" data-path="anay_6800.html"><a href="anay_6800.html#multi5"><i class="fa fa-check"></i><b>10.7.4</b> 光呼吸滞后性作图</a></li>
<li class="chapter" data-level="10.7.5" data-path="anay_6800.html"><a href="anay_6800.html#multi6"><i class="fa fa-check"></i><b>10.7.5</b> 补偿点计算</a></li>
<li class="chapter" data-level="10.7.6" data-path="anay_6800.html"><a href="anay_6800.html#multi7"><i class="fa fa-check"></i><b>10.7.6</b> 无光呼吸酶失活模块</a></li>
<li class="chapter" data-level="10.7.7" data-path="anay_6800.html"><a href="anay_6800.html#multi9"><i class="fa fa-check"></i><b>10.7.7</b> 酶失活作图</a></li>
<li class="chapter" data-level="10.7.8" data-path="anay_6800.html"><a href="anay_6800.html#multi10"><i class="fa fa-check"></i><b>10.7.8</b> 不同失活程度下补偿点计算</a></li>
</ul></li>
<li class="chapter" data-level="10.8" data-path="anay_6800.html"><a href="anay_6800.html#multi11"><i class="fa fa-check"></i><b>10.8</b> 时间延迟的扩散限制</a>
<ul>
<li class="chapter" data-level="10.8.1" data-path="anay_6800.html"><a href="anay_6800.html#multi12"><i class="fa fa-check"></i><b>10.8.1</b> 扩散限制滞后性</a></li>
</ul></li>
<li class="chapter" data-level="10.9" data-path="anay_6800.html"><a href="anay_6800.html#multi13"><i class="fa fa-check"></i><b>10.9</b> 扩散限制作图</a>
<ul>
<li class="chapter" data-level="10.9.1" data-path="anay_6800.html"><a href="anay_6800.html#multi14"><i class="fa fa-check"></i><b>10.9.1</b> 补偿点的计算</a></li>
<li class="chapter" data-level="10.9.2" data-path="anay_6800.html"><a href="anay_6800.html#multi15"><i class="fa fa-check"></i><b>10.9.2</b> 所有图形代码</a></li>
</ul></li>
<li class="chapter" data-level="10.10" data-path="anay_6800.html"><a href="anay_6800.html#fluro68"><i class="fa fa-check"></i><b>10.10</b> LI-6800 荧光数据分析</a>
<ul>
<li class="chapter" data-level="10.10.1" data-path="anay_6800.html"><a href="anay_6800.html#jiptest"><i class="fa fa-check"></i><b>10.10.1</b> jip test 的实现</a></li>
<li class="chapter" data-level="10.10.2" data-path="anay_6800.html"><a href="anay_6800.html#jiptest_pack"><i class="fa fa-check"></i><b>10.10.2</b> <code>jiptest</code> 软件包安装</a></li>
<li class="chapter" data-level="10.10.3" data-path="anay_6800.html"><a href="anay_6800.html#readfluor"><i class="fa fa-check"></i><b>10.10.3</b> <code>read_files</code> 及 <code>read_dcfiles</code> 函数</a></li>
<li class="chapter" data-level="10.10.4" data-path="anay_6800.html"><a href="anay_6800.html#testfluor"><i class="fa fa-check"></i><b>10.10.4</b> <code>jip_test</code> 及 <code>jip_dctest</code> 函数</a></li>
<li class="chapter" data-level="10.10.5" data-path="anay_6800.html"><a href="anay_6800.html#plotfluor"><i class="fa fa-check"></i><b>10.10.5</b> 图像查看函数</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="11" data-path="big-leaf.html"><a href="big-leaf.html"><i class="fa fa-check"></i><b>11</b> 大叶模型</a>
<ul>
<li class="chapter" data-level="11.1" data-path="big-leaf.html"><a href="big-leaf.html#leaf-scale-meas"><i class="fa fa-check"></i><b>11.1</b> 叶片尺度测量</a></li>
<li class="chapter" data-level="11.2" data-path="big-leaf.html"><a href="big-leaf.html#big-leaf-data"><i class="fa fa-check"></i><b>11.2</b> 数据的处理</a>
<ul>
<li class="chapter" data-level="11.2.1" data-path="big-leaf.html"><a href="big-leaf.html#single-data-big-leaf"><i class="fa fa-check"></i><b>11.2.1</b> 单个测量数据的处理</a></li>
<li class="chapter" data-level="11.2.2" data-path="big-leaf.html"><a href="big-leaf.html#big-leaf-data-MODEL"><i class="fa fa-check"></i><b>11.2.2</b> 大叶模型的数据处理</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="12" data-path="pca-anylysis.html"><a href="pca-anylysis.html"><i class="fa fa-check"></i><b>12</b> 大话 PCA</a>
<ul>
<li class="chapter" data-level="12.1" data-path="pca-anylysis.html"><a href="pca-anylysis.html#geom-pca"><i class="fa fa-check"></i><b>12.1</b> 几何解释</a></li>
<li class="chapter" data-level="12.2" data-path="pca-anylysis.html"><a href="pca-anylysis.html#alge-pca"><i class="fa fa-check"></i><b>12.2</b> 线性代数解释</a>
<ul>
<li class="chapter" data-level="12.2.1" data-path="pca-anylysis.html"><a href="pca-anylysis.html#egi-pca"><i class="fa fa-check"></i><b>12.2.1</b> 特征向量与特征值</a></li>
<li class="chapter" data-level="12.2.2" data-path="pca-anylysis.html"><a href="pca-anylysis.html#man_pca"><i class="fa fa-check"></i><b>12.2.2</b> 手动实现过程</a></li>
<li class="chapter" data-level="12.2.3" data-path="pca-anylysis.html"><a href="pca-anylysis.html#prcom"><i class="fa fa-check"></i><b>12.2.3</b> <code>prcomp</code> 的实现</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="13" data-path="sessioninfo.html"><a href="sessioninfo.html"><i class="fa fa-check"></i><b>13</b> 环境与配置</a></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>参考文献</a></li>
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<div id="photo_stomo" class="section level1" number="6">
<h1><span class="header-section-number">第 6 章</span> 光合气孔导度耦合模型</h1>
<p><span class="citation">Remko A. Duursma (<a href="#ref-Duursma2015Plantecophys" role="doc-biblioref">2015</a>)</span> 对于气体交换耦合模型的简述如下 <a href="references.html#fn11" class="footnote-ref" id="fnref11"><sup>11</sup></a>：</p>
<ul>
<li>对于 FvCB 模型有：</li>
</ul>
<p><span class="math display" id="eq:minfvcb">\[\begin{equation}
A_n = min(A_c, A_j)-R_d
\tag{6.1}
\end{equation}\]</span></p>
<ul>
<li>在假定 gm 为恒定的前提下：</li>
</ul>
<p><span class="math display" id="eq:cgm">\[\begin{equation}
C_c = C_i - \frac{A_n}{g_m}
\tag{6.2}
\end{equation}\]</span></p>
<ul>
<li>根据 Ficker 定理</li>
</ul>
<p><span class="math display" id="eq:ficker">\[\begin{equation}
A_n = \frac{g_s}{1.6}(C_a - C_i)
\tag{6.3}
\end{equation}\]</span></p>
<p>以及前文 <a href="stomotal_sim.html#ballberry">4.1</a> 提到的气孔导度模型</p>
<p><span class="math display" id="eq:driver">\[\begin{equation}
g_s = g_0 + g_1 \frac{A_n}{C_a} f(D)
\tag{6.4}
\end{equation}\]</span></p>
<p>整合公式 <a href="photo_stomo.html#eq:minfvcb">(6.1)</a>, <a href="photo_stomo.html#eq:cgm">(6.2)</a>, <a href="photo_stomo.html#eq:ficker">(6.3)</a> 和 <a href="photo_stomo.html#eq:driver">(6.4)</a>，气体交换耦合模型有很多更大尺度上的应用，例如 <span class="citation">R. A. Duursma and Medlyn (<a href="#ref-Duursma2012MAESPA" role="doc-biblioref">2012</a>)</span> 和 wang1998a，可用于预测 An，gs 和蒸腾速率对主要环境驱动因子的响应（除土壤水分），并包含了主要的叶片性状（g1，V<sub>cmax</sub>, J<sub>max</sub>, R<sub>d</sub> 以及他们的温度依赖性）。</p>
<div id="photosyn" class="section level2" number="6.1">
<h2><span class="header-section-number">6.1</span> <code>Photosyn</code> 函数</h2>
<p>Photosyn 为耦合的光合–气孔导度模型，基于 Farquhar 光合模型和 Ball-Berry 气孔导度模型。</p>
<div class="sourceCode" id="cb62"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb62-1"><a href="photo_stomo.html#cb62-1" aria-hidden="true" tabindex="-1"></a><span class="fu">Photosyn</span>(<span class="at">VPD =</span> <span class="fl">1.5</span>, <span class="at">Ca =</span> <span class="dv">400</span>, <span class="at">PPFD =</span> <span class="dv">1500</span>,</span>
<span id="cb62-2"><a href="photo_stomo.html#cb62-2" aria-hidden="true" tabindex="-1"></a>         <span class="at">Tleaf =</span> <span class="dv">25</span>, <span class="at">Patm =</span> <span class="dv">100</span>,<span class="at">RH =</span> <span class="cn">NULL</span>,</span>
<span id="cb62-3"><a href="photo_stomo.html#cb62-3" aria-hidden="true" tabindex="-1"></a>         <span class="at">gsmodel =</span> <span class="fu">c</span>(<span class="st">&quot;BBOpti&quot;</span>, <span class="st">&quot;BBLeuning&quot;</span>, </span>
<span id="cb62-4"><a href="photo_stomo.html#cb62-4" aria-hidden="true" tabindex="-1"></a>                     <span class="st">&quot;BallBerry&quot;</span>, <span class="st">&quot;BBdefine&quot;</span>),</span>
<span id="cb62-5"><a href="photo_stomo.html#cb62-5" aria-hidden="true" tabindex="-1"></a>         <span class="at">g1 =</span> <span class="dv">4</span>, <span class="at">g0 =</span> <span class="dv">0</span>, <span class="at">gk =</span> <span class="fl">0.5</span>, <span class="at">vpdmin =</span> <span class="fl">0.5</span>,</span>
<span id="cb62-6"><a href="photo_stomo.html#cb62-6" aria-hidden="true" tabindex="-1"></a>         <span class="at">D0 =</span> <span class="dv">5</span>, <span class="at">GS =</span> <span class="cn">NULL</span>, <span class="at">BBmult =</span> <span class="cn">NULL</span>, </span>
<span id="cb62-7"><a href="photo_stomo.html#cb62-7" aria-hidden="true" tabindex="-1"></a>         <span class="at">alpha =</span> <span class="fl">0.24</span>, <span class="at">theta =</span> <span class="fl">0.85</span>, <span class="at">Jmax =</span> <span class="dv">100</span>,</span>
<span id="cb62-8"><a href="photo_stomo.html#cb62-8" aria-hidden="true" tabindex="-1"></a>         <span class="at">Vcmax =</span> <span class="dv">50</span>, <span class="at">gmeso =</span> <span class="cn">NULL</span>, <span class="at">TPU =</span> <span class="dv">1000</span>, </span>
<span id="cb62-9"><a href="photo_stomo.html#cb62-9" aria-hidden="true" tabindex="-1"></a>         <span class="at">alphag =</span> <span class="dv">0</span>, <span class="at">Rd0 =</span> <span class="fl">0.92</span>, <span class="at">Q10 =</span> <span class="fl">1.92</span>,</span>
<span id="cb62-10"><a href="photo_stomo.html#cb62-10" aria-hidden="true" tabindex="-1"></a>         <span class="at">Rd =</span> <span class="cn">NULL</span>, <span class="at">TrefR =</span> <span class="dv">25</span>, <span class="at">Rdayfrac =</span> <span class="dv">1</span>, </span>
<span id="cb62-11"><a href="photo_stomo.html#cb62-11" aria-hidden="true" tabindex="-1"></a>         <span class="at">EaV =</span> <span class="fl">82620.87</span>, <span class="at">EdVC =</span> <span class="dv">0</span>, <span class="at">delsC =</span> <span class="fl">645.1013</span>, </span>
<span id="cb62-12"><a href="photo_stomo.html#cb62-12" aria-hidden="true" tabindex="-1"></a>         <span class="at">EaJ =</span> <span class="fl">39676.89</span>, <span class="at">EdVJ =</span> <span class="fl">2e+05</span>, <span class="at">delsJ =</span> <span class="fl">641.3615</span>,</span>
<span id="cb62-13"><a href="photo_stomo.html#cb62-13" aria-hidden="true" tabindex="-1"></a>         <span class="at">GammaStar =</span> <span class="cn">NULL</span>, <span class="at">Km =</span> <span class="cn">NULL</span>, <span class="at">Ci =</span> <span class="cn">NULL</span>, </span>
<span id="cb62-14"><a href="photo_stomo.html#cb62-14" aria-hidden="true" tabindex="-1"></a>         <span class="at">Tcorrect =</span> <span class="cn">TRUE</span>,<span class="at">returnParsOnly =</span> <span class="cn">FALSE</span>,</span>
<span id="cb62-15"><a href="photo_stomo.html#cb62-15" aria-hidden="true" tabindex="-1"></a>         <span class="at">whichA =</span> <span class="fu">c</span>(<span class="st">&quot;Ah&quot;</span>, <span class="st">&quot;Amin&quot;</span>, <span class="st">&quot;Ac&quot;</span>, <span class="st">&quot;Aj&quot;</span>))</span>
<span id="cb62-16"><a href="photo_stomo.html#cb62-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb62-17"><a href="photo_stomo.html#cb62-17" aria-hidden="true" tabindex="-1"></a><span class="fu">Aci</span>(Ci, ...)</span></code></pre></div>
<p>因为是光合气孔导度模型的耦合，故而参数与之前的函数相同，参见 <a href="response_fit.html#fitaci-p">3.5.2</a> 和 <a href="stomotal_sim.html#fitbb-p">4.4</a> 部分的内容。</p>
<div id="photo_exam" class="section level3" number="6.1.1">
<h3><span class="header-section-number">6.1.1</span> <code>Photosyn</code> 使用举例</h3>
<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb63-1"><a href="photo_stomo.html#cb63-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(plantecophys)</span>
<span id="cb63-2"><a href="photo_stomo.html#cb63-2" aria-hidden="true" tabindex="-1"></a><span class="co"># 仅使用下面几个参数运行模型</span></span>
<span id="cb63-3"><a href="photo_stomo.html#cb63-3" aria-hidden="true" tabindex="-1"></a><span class="co">#（其他参数使用默认值）</span></span>
<span id="cb63-4"><a href="photo_stomo.html#cb63-4" aria-hidden="true" tabindex="-1"></a><span class="co"># 利用已测量或计算的参数</span></span>
<span id="cb63-5"><a href="photo_stomo.html#cb63-5" aria-hidden="true" tabindex="-1"></a><span class="fu">Photosyn</span>(<span class="at">VPD=</span><span class="dv">2</span>, <span class="at">g1=</span><span class="dv">4</span>, <span class="at">Ca=</span><span class="dv">500</span>)</span></code></pre></div>
<pre><code>##         Ci    ALEAF        GS    ELEAF       Ac       Aj   Ap   Rd VPD Tleaf
## 1 369.3981 14.19466 0.1706377 3.412753 15.12654 17.03685 1000 0.92   2    25
##    Ca       Cc PPFD Patm
## 1 500 369.3981 1500  100</code></pre>
<div class="sourceCode" id="cb65"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb65-1"><a href="photo_stomo.html#cb65-1" aria-hidden="true" tabindex="-1"></a><span class="co"># 部分参数相同，而某一参数或某几个参数不同时，</span></span>
<span id="cb65-2"><a href="photo_stomo.html#cb65-2" aria-hidden="true" tabindex="-1"></a><span class="co"># 可以将不同的参数设置为一个序列（vectors）</span></span>
<span id="cb65-3"><a href="photo_stomo.html#cb65-3" aria-hidden="true" tabindex="-1"></a>r <span class="ot">&lt;-</span> <span class="fu">Photosyn</span>(<span class="at">VPD=</span><span class="fu">seq</span>(<span class="fl">0.5</span>, <span class="dv">4</span>, <span class="at">length=</span><span class="dv">25</span>), </span>
<span id="cb65-4"><a href="photo_stomo.html#cb65-4" aria-hidden="true" tabindex="-1"></a>              <span class="at">Vcmax=</span><span class="dv">50</span>, <span class="at">Jmax=</span><span class="dv">100</span>)</span>
<span id="cb65-5"><a href="photo_stomo.html#cb65-5" aria-hidden="true" tabindex="-1"></a><span class="fu">with</span>(r, <span class="fu">plot</span>(VPD, ALEAF, <span class="at">type=</span><span class="st">&#39;l&#39;</span>))</span></code></pre></div>
<div class="figure"><span style="display:block;" id="fig:vpd"></span>
<img src="bookdown_files/figure-html/vpd-1.png" alt="VPD VS. An" width="672" />
<p class="caption">
图 6.1: VPD VS. An
</p>
</div>
<p>不同 VPD 下的光合速率见 <a href="photo_stomo.html#fig:vpd">6.1</a>。</p>
<div class="sourceCode" id="cb66"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb66-1"><a href="photo_stomo.html#cb66-1" aria-hidden="true" tabindex="-1"></a><span class="co"># 设定叶肉导度的拟合</span></span>
<span id="cb66-2"><a href="photo_stomo.html#cb66-2" aria-hidden="true" tabindex="-1"></a>run1 <span class="ot">&lt;-</span> <span class="fu">Photosyn</span>(<span class="at">PPFD=</span><span class="fu">seq</span>(<span class="dv">50</span>,<span class="dv">1000</span>,<span class="at">length=</span><span class="dv">25</span>), </span>
<span id="cb66-3"><a href="photo_stomo.html#cb66-3" aria-hidden="true" tabindex="-1"></a>                 <span class="at">gmeso=</span><span class="fl">0.15</span>, <span class="at">Vcmax=</span><span class="dv">40</span>, <span class="at">Jmax=</span><span class="dv">85</span>)</span>
<span id="cb66-4"><a href="photo_stomo.html#cb66-4" aria-hidden="true" tabindex="-1"></a><span class="fu">with</span>(run1, <span class="fu">plot</span>(PPFD, GS, <span class="at">type=</span><span class="st">&#39;l&#39;</span>))</span></code></pre></div>
<div class="figure"><span style="display:block;" id="fig:ppfd-1"></span>
<img src="bookdown_files/figure-html/ppfd-1.png" alt="PPFD VS. GS" width="672" />
<p class="caption">
图 6.2: PPFD VS. GS
</p>
</div>
<div class="sourceCode" id="cb67"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb67-1"><a href="photo_stomo.html#cb67-1" aria-hidden="true" tabindex="-1"></a><span class="co"># 运行ACi曲线数据（提供Ci值而不是计算）</span></span>
<span id="cb67-2"><a href="photo_stomo.html#cb67-2" aria-hidden="true" tabindex="-1"></a>arun1 <span class="ot">&lt;-</span> <span class="fu">Aci</span>(<span class="at">Ci=</span><span class="fu">seq</span>(<span class="dv">50</span>, <span class="dv">1200</span>, <span class="at">length=</span><span class="dv">101</span>), </span>
<span id="cb67-3"><a href="photo_stomo.html#cb67-3" aria-hidden="true" tabindex="-1"></a>             <span class="at">Vcmax=</span><span class="dv">40</span>, <span class="at">Jmax=</span><span class="dv">85</span>)</span>
<span id="cb67-4"><a href="photo_stomo.html#cb67-4" aria-hidden="true" tabindex="-1"></a>arun2 <span class="ot">&lt;-</span> <span class="fu">Aci</span>(<span class="at">Ci=</span><span class="fu">seq</span>(<span class="dv">50</span>, <span class="dv">1200</span>, <span class="at">length=</span><span class="dv">101</span>), </span>
<span id="cb67-5"><a href="photo_stomo.html#cb67-5" aria-hidden="true" tabindex="-1"></a>             <span class="at">Vcmax=</span><span class="dv">30</span>, <span class="at">Jmax=</span><span class="dv">70</span>)</span>
<span id="cb67-6"><a href="photo_stomo.html#cb67-6" aria-hidden="true" tabindex="-1"></a><span class="fu">with</span>(arun1, <span class="fu">plot</span>(Ci, ALEAF, <span class="at">type=</span><span class="st">&#39;l&#39;</span>))</span>
<span id="cb67-7"><a href="photo_stomo.html#cb67-7" aria-hidden="true" tabindex="-1"></a><span class="fu">with</span>(arun2, <span class="fu">points</span>(Ci, ALEAF, <span class="at">type=</span><span class="st">&#39;l&#39;</span>, <span class="at">lty=</span><span class="dv">5</span>))</span></code></pre></div>
<div class="figure"><span style="display:block;" id="fig:ppfd-2"></span>
<img src="bookdown_files/figure-html/ppfd-2.png" alt="PPFD VS. GS" width="672" />
<p class="caption">
图 6.3: PPFD VS. GS
</p>
</div>
<p>不同 ci 下的光合速率见 <a href="#fig:ppfd"><strong>??</strong></a>。</p>
<div class="sourceCode" id="cb68"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb68-1"><a href="photo_stomo.html#cb68-1" aria-hidden="true" tabindex="-1"></a><span class="co"># 找出CO2需求和供给的交叉点</span></span>
<span id="cb68-2"><a href="photo_stomo.html#cb68-2" aria-hidden="true" tabindex="-1"></a><span class="co"># 设定部分参数</span></span>
<span id="cb68-3"><a href="photo_stomo.html#cb68-3" aria-hidden="true" tabindex="-1"></a>gs <span class="ot">&lt;-</span> <span class="fl">0.2</span> <span class="co"># 对水的气孔导度</span></span>
<span id="cb68-4"><a href="photo_stomo.html#cb68-4" aria-hidden="true" tabindex="-1"></a>Ca <span class="ot">&lt;-</span> <span class="dv">400</span> <span class="co"># 外部CO2</span></span>
<span id="cb68-5"><a href="photo_stomo.html#cb68-5" aria-hidden="true" tabindex="-1"></a>gctogw <span class="ot">&lt;-</span> <span class="fl">1.57</span> <span class="co"># 转换系数</span></span>
<span id="cb68-6"><a href="photo_stomo.html#cb68-6" aria-hidden="true" tabindex="-1"></a>gc <span class="ot">&lt;-</span> gs <span class="sc">/</span> gctogw <span class="co"># 对 CO2 的气孔导度</span></span>
<span id="cb68-7"><a href="photo_stomo.html#cb68-7" aria-hidden="true" tabindex="-1"></a><span class="co"># 需求曲线</span></span>
<span id="cb68-8"><a href="photo_stomo.html#cb68-8" aria-hidden="true" tabindex="-1"></a>p <span class="ot">&lt;-</span> <span class="fu">Aci</span>(<span class="fu">seq</span>(<span class="dv">60</span>,<span class="dv">500</span>,<span class="at">length=</span><span class="dv">101</span>), <span class="at">Ca=</span><span class="dv">400</span>)</span>
<span id="cb68-9"><a href="photo_stomo.html#cb68-9" aria-hidden="true" tabindex="-1"></a><span class="co"># 提供气孔导度及交叉点</span></span>
<span id="cb68-10"><a href="photo_stomo.html#cb68-10" aria-hidden="true" tabindex="-1"></a>g <span class="ot">&lt;-</span> <span class="fu">Photosyn</span>(<span class="at">GS=</span>gs, <span class="at">Ca=</span>Ca)</span>
<span id="cb68-11"><a href="photo_stomo.html#cb68-11" aria-hidden="true" tabindex="-1"></a><span class="co"># 交叉点可视化</span></span>
<span id="cb68-12"><a href="photo_stomo.html#cb68-12" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">yaxs=</span><span class="st">&quot;i&quot;</span>)</span>
<span id="cb68-13"><a href="photo_stomo.html#cb68-13" aria-hidden="true" tabindex="-1"></a><span class="fu">with</span>(p, <span class="fu">plot</span>(Ci, ALEAF, <span class="at">type=</span><span class="st">&#39;l&#39;</span>, </span>
<span id="cb68-14"><a href="photo_stomo.html#cb68-14" aria-hidden="true" tabindex="-1"></a>             <span class="at">ylim=</span><span class="fu">c</span>(<span class="dv">0</span>,<span class="fu">max</span>(ALEAF))))</span>
<span id="cb68-15"><a href="photo_stomo.html#cb68-15" aria-hidden="true" tabindex="-1"></a><span class="fu">with</span>(g, <span class="fu">points</span>(Ci, ALEAF, <span class="at">pch=</span><span class="dv">19</span>, <span class="at">col=</span><span class="st">&quot;red&quot;</span>))</span>
<span id="cb68-16"><a href="photo_stomo.html#cb68-16" aria-hidden="true" tabindex="-1"></a><span class="fu">abline</span>(gc <span class="sc">*</span> Ca, <span class="sc">-</span>gc, <span class="at">lty=</span><span class="dv">5</span>)</span>
<span id="cb68-17"><a href="photo_stomo.html#cb68-17" aria-hidden="true" tabindex="-1"></a><span class="fu">legend</span>(<span class="st">&quot;topleft&quot;</span>, <span class="fu">c</span>(<span class="fu">expression</span>(</span>
<span id="cb68-18"><a href="photo_stomo.html#cb68-18" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;Demand:&quot;</span><span class="sc">~</span><span class="er">~</span>A<span class="sc">==</span><span class="fu">f</span>(C[i])),</span>
<span id="cb68-19"><a href="photo_stomo.html#cb68-19" aria-hidden="true" tabindex="-1"></a>   <span class="fu">expression</span>(<span class="st">&quot;Supply:&quot;</span><span class="sc">~</span><span class="er">~</span>A<span class="sc">==</span>g[c]<span class="sc">*</span>(C[a]<span class="sc">-</span>C[i])),</span>
<span id="cb68-20"><a href="photo_stomo.html#cb68-20" aria-hidden="true" tabindex="-1"></a>              <span class="st">&quot;Operating point&quot;</span>),</span>
<span id="cb68-21"><a href="photo_stomo.html#cb68-21" aria-hidden="true" tabindex="-1"></a>   <span class="at">lty=</span><span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">5</span>,<span class="sc">-</span><span class="dv">1</span>),<span class="at">pch=</span><span class="fu">c</span>(<span class="sc">-</span><span class="dv">1</span>,<span class="sc">-</span><span class="dv">1</span>,<span class="dv">19</span>),</span>
<span id="cb68-22"><a href="photo_stomo.html#cb68-22" aria-hidden="true" tabindex="-1"></a>   <span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;black&quot;</span>,<span class="st">&quot;black&quot;</span>,<span class="st">&quot;red&quot;</span>),</span>
<span id="cb68-23"><a href="photo_stomo.html#cb68-23" aria-hidden="true" tabindex="-1"></a>   <span class="at">bty=</span><span class="st">&#39;n&#39;</span>, <span class="at">cex=</span><span class="fl">0.9</span>)</span></code></pre></div>
<div class="figure"><span style="display:block;" id="fig:supply"></span>
<img src="bookdown_files/figure-html/supply-1.png" alt="supply VS. demand" width="672" />
<p class="caption">
图 6.4: supply VS. demand
</p>
</div>
<p>需求与供给的作图 <a href="photo_stomo.html#fig:supply">6.4</a>。</p>
</div>
</div>
<div id="photsyneb" class="section level2" number="6.2">
<h2><span class="header-section-number">6.2</span> <code>PhotosynEB</code> 函数</h2>
<p>使用同 <code>Photosyn</code>，只不过使用能量平衡法来计算叶温。
目前版本尚存在bug，不能直接提供 GS 来计算，否则会出现未知错误。</p>
</div>
<div id="photosyntuzet" class="section level2" number="6.3">
<h2><span class="header-section-number">6.3</span> <code>PhotosynTuzet</code> 函数</h2>
<p>同样为光合气孔导度耦合模型，只不过基于 <span class="citation">Tuzet, Perrier, and Leuning (<a href="#ref-tuzet2003a" role="doc-biblioref">2003</a>)</span> 的气孔导度模型，现将其描述如下：</p>
<p><span class="math display" id="eq:tuzet">\[\begin{equation}
g_{co2} = g_0 + \frac{a A}{C_i - \Gamma} f_{\Psi v}
\tag{6.5}
\end{equation}\]</span></p>
<p>其中 g<sub>co2</sub> 为对 CO<sub>2</sub> 的气孔导度， g<sub>0</sub> 是残余导度（residual conductance）(在补偿点时限制 g<sub>CO2</sub> 的值）， A 为光合速率，C<sub>i</sub> 为胞间二氧化碳浓度，<span class="math inline">\(\Gamma\)</span> 为 CO<sub>2</sub> 补偿点，a 是经验系数。</p>
<p>一个根据经验的逻辑方程用于描述气孔对水势的敏感性：</p>
<p><span class="math display" id="eq:ftuzet">\[\begin{equation}
f_{\Psi v} = \frac{1 + exp(s_f \Psi_f)}{1 + exp(s_f(\Psi_f - \Psi_v))}
\tag{6.6}
\end{equation}\]</span></p>
<p><span class="math inline">\(\Psi_v\)</span> 是指叶片水势，<span class="math inline">\(\Psi_f\)</span> 是参比势能， 该方程假设在水势接近于 0 时，气孔对叶片水势不敏感，并且气孔随着 <span class="math inline">\(\Psi_v\)</span> 的下降快速关闭。<span class="math inline">\(\Psi_f\)</span> 和 <span class="math inline">\(s_f\)</span> (曲线形状参数) 依赖于不同物种的形态学适应以及生长过程中所处的环境。</p>
<div id="photosyntuzet_para" class="section level3" number="6.3.1">
<h3><span class="header-section-number">6.3.1</span> <code>PhotosynTuzet</code> 的参数</h3>
<p>除 <span class="citation">Tuzet, Perrier, and Leuning (<a href="#ref-tuzet2003a" role="doc-biblioref">2003</a>)</span> 模型中使用的参数外，其他参数都继承了 <code>Photosyn</code> 的参数</p>
<div class="sourceCode" id="cb69"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb69-1"><a href="photo_stomo.html#cb69-1" aria-hidden="true" tabindex="-1"></a><span class="fu">PhotosynTuzet</span>(<span class="at">g1 =</span> <span class="dv">8</span>, <span class="at">Ca =</span> <span class="dv">400</span>, <span class="at">psis =</span> <span class="dv">0</span>,</span>
<span id="cb69-2"><a href="photo_stomo.html#cb69-2" aria-hidden="true" tabindex="-1"></a>              <span class="at">kl =</span> <span class="dv">2</span>, <span class="at">sf =</span> <span class="dv">3</span>, <span class="at">psif =</span> <span class="sc">-</span><span class="dv">2</span>,</span>
<span id="cb69-3"><a href="photo_stomo.html#cb69-3" aria-hidden="true" tabindex="-1"></a>...)</span></code></pre></div>
<ul>
<li>g1：斜率参数，要远比 <code>fitBB</code> 中的大。</li>
<li>Ca：外界大气 CO<sub>2</sub> 浓度</li>
<li>psis，土壤水势（Mpa）。</li>
<li>kl：Leaf-speciﬁc hydraulic conductance（叶片导水参数 (<span class="math inline">\(mmol \cdot m^{-2} \cdot s^{-1} \cdot MPa^{-1}\)</span>)，叶片蒸腾量、叶片面积及叶片水势计算）。</li>
<li>sf：曲线形状参数。</li>
<li>在气孔导度为最大值 50% 时的叶片水势。</li>
</ul>

</div>
</div>
</div>
<h3>参考文献</h3>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-Duursma2012MAESPA" class="csl-entry">
Duursma, R. A., and B. E. Medlyn. 2012. <span>“MAESPA: A Model to Study Interactions Between Water Limitation, Environmental Drivers and Vegetation Function at Tree and Stand Levels, with an Example Application to CO<span class="math inline">\(_2\)</span> Drought Interactions.”</span> <em>Geoscientific Model Development Discussions</em> 5 (4): 919–40.
</div>
<div id="ref-Duursma2015Plantecophys" class="csl-entry">
Duursma, Remko A. 2015. <span>“Plantecophys-an r Package for Analysing and Modelling Leaf Gas Exchange Data.”</span> <em>Plos One</em> 10 (11): e0143346.
</div>
<div id="ref-tuzet2003a" class="csl-entry">
Tuzet, A, A Perrier, and R Leuning. 2003. <span>“A Coupled Model of Stomatal Conductance, Photosynthesis and Transpiration.”</span> <em>Plant Cell and Environment</em> 26 (7): 1097–1116.
</div>
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